Arrow's Theorem, countably many agents, and more visible invisible dictators

For infinite societies, Fishburn (1970), Kirman and Sondermann (1972), and Armstrong (1980) gave a nonconstructive proof of the existence of a social welfare function satisfying Arrowfs conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving a concrete example of such a function, and (ii) showing how to compute, from a description of a profile on a pair of alternatives, which alternative is socially preferred under the function. The introduction of a certain goracleh resolves Miharafs impossibility result (1997) about computability of social welfare functions.Arrow impossibility theorem, Turing computability, recursion theory, oracle algorithms, free ultrafilters

Nonanonymity and sensitivity of computable simple games

This paper investigates algorithmic computability of simple games (voting games). It shows that (i) games with a finite carrier are computable, (ii) computable games have both finite winning coalitions and cofinite losing coalitions, and (iii) computable games violate any conceivable notion of anonymity, including finite anonymity and measurebased anonymity. The paper argues that computable games are excluded from the intuitive class of gniceh infinite games, employing the notion of ginsensitivityh\-equal treatment of any two coalitions that differ only on a finite set.Voting games, infinitely many players, ultrafilters, recursion theory, Turing computability, finite carriers, finite winning coalitions, algorithms

Coalitionally strategyproof functions depend only on the most-preferred alternatives

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy gtops only.h That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third, . . . , or the least. The functions are defined on the domain of profiles measurable with respect to a Boolean algebra of coalitions. The unrestricted domain of profiles is an example of such a domain. I also prove an extension theorem.Gibbard-Satterthwaite theorem, dominant strategy implementation, social choice functions, infinitely large societies, tops only

Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof

This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies. The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is gdescribable.h The gdescribableh coalitions are assumed to form a countable Boolean algebra. The paper discusses oligarchical characteristics of the function, employing a specific interpretation of an infinite society. The discussion clarifies within a single framework a connection between the negative result (the Gibbard-Satterthwaite theorem) for finite societies and the positive result for infinite ones.Gibbard-Satterthwaite theorem, cheatproofness, dominant strategy implementation, strategy-proof social choice functions, plurality rule, infinitely large societies, countable Boolean algebras of coalitions, free ultrafilters, models of knowledge, partitional information functions.

Computability of simple games: A characterization and application to the core

It was shown earlier that the class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games, strengthens the earlier result that computable games violate anonymity, and gives examples showing that the above inclusions are strict. It also extends Nakamura’s theorem about the nonemptyness of the core and shows that computable simple games have a finite Nakamura number, implying that the number of alternatives that the players can deal with rationally is restricted

Computability of simple games: A complete investigation of the sixty-four possibilities

Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and algorithmic computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable ones and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms.Comment: 25 page

Arrow's theorem, Weglorz' models and the axiom of choice

Applying Weglorz' models of set theory without the axiom of choice, we investigate Arrow-type social welfare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying "finite discrimination", if and only if in Weglorz' model there is a free ultrafilter on a set representing the individuals.Arrow impossibility theorem, anonymity, ecological welfare functions, axiomatic set theory, ultrafilters, Weglorz's models, permutation models

Affidavit of CDAT Counsel

A sworn affidavit of Counsel in Support of Coeur d\u27Alene Tribe\u27s Responsive Briefing and exhibits 1-13 in support thereof

A search for cyclotron resonance features with INTEGRAL

We present an INTEGRAL observation of the Cen-Crux region in order to search the electron cyclotron resonance scattering features from the X-ray binary pulsars. During the AO1 200ks observation, we clearly detected 4 bright X-ray binaries, 1 Seyfert Galaxy, and 4 new sources in the field of view. Especially from GX301-2, the cyclotron resonance feature is detected at about 37 keV, and width of 3--4 keV. In addition, the depth of the resonance feature strongly depends on the X-ray luminosity. This is the first detection of luminosity dependence of the resonance depth. The cyclotron resonance feature is marginally detected from 1E1145.1-6141. Cen X-3 was very dim during the observation and poor statistics disable us to detect the resonance features.These are first INTEGRAL results of searching for the cyclotron resonance feature.Comment: 4pages, 8figures, To be published in the Proceedings of the 5th INTEGRAL Workshop: "The INTEGRAL Universe", February 16-20, 2004, Munic